On the realistic validation of photometric redshifts, or why Teddy will never be Happy

The challenge of accurate photometric redshift (photo-z) validation is the elephant in the room that needs to be solved to ensure the full exploitation of upcoming astronomical surveys. Two of the main problems encountered in the development of photo-z techniques are the lack of spectroscopic coverage in feature space (e.g. colours and magnitudes) and the mismatch between photometric error distributions associated with the spectroscopic and photometric samples. Although these issues are well known, there is currently no standard benchmark allowing a quantifiable diagnostic of their impact on the final photo-z estimation. In this work, we present two galaxy catalogues built to enable a more demanding and realistic test of photo-z methods. Using photometry from the Sloan Digital Sky Survey and spectroscopy from a collection of sources, we constructed datasets which mimic the biases between the underlying probability distribution of the real spectroscopic and photometric sample while also possessing spectroscopic measurements. We demonstrate the potential of these catalogues by submitting them to the scrutiny of different photo-z methods, including machine learning (ML) and template fitting approaches. Beyond the expected bad results from most ML algorithms for cases with missing coverage in feature space, we were also able to recognize the superiority of global models in the same situation and the general failure across all types of methods when incomplete coverage is convoluted with the presence of photometric errors - a data situation which photo-z methods were not trained to deal with up to now and which must be addressed by future large scale surveys. Our catalogues represent the first controlled environment allowing a straightforward implementation of such tests. The data are publicly available within the COINtoolbox (this https URL).